I think that it's correct. Here is a picture which George Beldecos, an authority on Greek ODM, gave me (it's in his book, Hellenic Orders, Decorations and Medals 1991, & he's given me permission to use it, although it has been 'poached' and reproduced on the internet elsewhere!):
The disparity of design between collar badge and star is the same as in the eBay offering.
It seems to be that the star that you get with the collar is of a completely different design to everything else in the order - the badges of other classes are of similar design to the collar badge, and the centres of the Grand Cross and Knight Commander stars are again like the badges.